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Negation for Expressivists: A Collection
of Problems with a Suggestion
for their Solution
James Dreier
Crucial to the solution of various problems for expressivism is the development of a coherent semantics for negation. Nicholas Unwin (2001)
explained why Allan Gibbard’s program in Wise Choices, Apt Feelings was
not up to the task. Briefly, the problem is that there are three ways to
‘negate’ a sentence like
(M)
Miss Manners thinks one must write thank you notes by hand.
The three are:
(N1 ) Miss Manners believes one must not write thank you notes
by hand.
(N2 ) Miss Manners believes it is not so that one must write thank
you notes by hand.
(N3 ) Miss Manners does not believe one must write thank you notes
by hand.
But the resources available in Gibbard’s scheme seem to allow the construction of only two, most plausibly (N1 ) and (N3 ), with no way to interpret
(N2 ). From a logical point of view, we can think of requirement and
permission as operators on sentences (or on infinitives or participles). The
This paper benefited enormously from discussion at the Madison Metaethics Workshop, Oct. 2004, and also from audiences at the University of Maryland and Princeton
University. I thank especially Jim Pryor for good counter-examples and Nick Unwin for
some emailed comments on an early draft.
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1. The Negation Problem
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operators are duals, so that to define one operator in terms of the other we
need not just internal negation, but external as well. Compare the problem
of defining possibility in terms of necessity: we can say that !A is defined as
¬"¬A, but only if we already know what it means to negate the possibility
operator. If, on the other hand, we know independently what necessity and
possibility are, then we can define external negation: ¬!A is defined as
"¬A and ¬"A is defined as !¬A.
The present problem is similar. We can use R• and P as operators for
requirement and permission, and then note that RA is (defined as) ¬P¬A;
more to the point, ¬RA is (defined as) P¬A and ¬PA is (defined as)
R¬A. Here the externally negated sentences are explained in terms of other
sentences whose negations are all internal; that is to say, the negation signs
occur only inside the operators, and no operators are negated. These dual
definitions are useful. Each sentence with a primary operator (an operator
with scope over the rest of the sentence) expresses an attitude, expressivists
tell us. The nature of the operator gives the nature of the attitude. If
Miss Manners tells you that you must write thank you notes by hand, her
sentence (‘‘You must write thank you notes by hand’’) expresses an attitude,
signaled by ‘must’, toward writing thank you notes by hand. If she tells you
that you must not write thank you notes by hand, then she is expressing
that same ‘must’ attitude again toward not writing thank you notes by
hand. The negation is internal, so no new explanation is necessary. But
what state of mind is expressed by the statement ‘‘It is not so that one must
write thank you notes by hand’’? If she said that, Miss Manners would be
giving voice to the belief described by (N2 ). It’s all very well to say, as one
might, that Miss Manners expresses the negation of the ‘must’ attitude (the
attitude of ‘requiring’, let’s say) toward the same kind of action (writing
thank you notes by hand). But how are attitudes negated? Expressivists
need no special story about how to negate propositions, or actions, since
those negations are not specific to expressivism. But there is no ordinary
language or commonsense notion of the negation of an attitude.
It is tempting to think that the negation of an attitude might be the
absence of that attitude. Compare belief: besides the ‘internal negation’ that
takes a belief that A to a belief that ¬A, there is also the external kind taking
belief that A to failing to believe that A. Could the negation of requiring
something be the attitude of not requiring it? Not in our context. True,
(N3 ) is the negation of (M). It is the real negation, the contradictory of
(M). But (N3 ) is not (N2 ), which is what we wanted.
I said that the dual definitions are useful; here’s how. If we know what
attitude is expressed by ‘R’ (call it requirement) and we know what attitude
is expressed by ‘P’ (call it toleration), then an account of ‘negated attitudes’
follows naturally. The negation of a tolerant attitude toward A, so to
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speak, will be the attitude of requiring ¬A, and conversely the negation of
requiring A is tolerating ¬A. So if we can just help ourselves to the two
attitudes, negation falls out. Since those two attitudes are perfectly ordinary,
commonsense attitudes, one approach would be simply to take them as
primitive.1
But in fact, this approach is problematic. It leaves mysterious why the two
attitudes, toleration and requirement, are related to one another logically.
Why is there any incoherence in tolerating something and also requiring
its contradictory? That is what we are supposed to explain. It’s no good
just to posit that they are incoherent. How is it, anyway, that attitudes are
logically related? As Bob Hale (1993) asked, can there be a logic of attitudes?
This question, I think, is the same as the question of negation.
In Thinking How to Live, Gibbard introduces a revised approach to norm
expressivism. The new view differs from the old in a number of ways,
although the core ideas are all still in place. Central to the new approach is
the development of the idea of disagreement, which Gibbard thinks is the
key to all sorts of problems. Among these problems is Unwin’s problem
of negation. If expressivists can appeal to a notion of disagreeing with
someone’s attitude (maybe one’s own), then negation flows naturally into
the scheme. How? Rather than take toleration and requirement as primitive
attitudes, we can think of tolerating ¬A as disagreeing with requiring A.
External negation corresponds to disagreement. The attitude expressed by
the external negation of a sentence (with a primary operator) is disagreement
with the attitude expressed by the sentence. In this way, the attitudes are
related to each other structurally, as negations ought to be, and the factor
by which they are related, disagreement, looks to have the right features to
correspond to negation.
Suppose, then, that you judge that one must write thank you notes by
hand. Your state of mind, according to Gibbard, is one of planning to write
thank you notes by hand (if the occasion arises). Miss Manners disagrees.
(N2 ) says that she does. Her state of mind is: disagreeing with your plan.
One way she might disagree, of course, is by definitely planning not to
write thank you notes by hand, in which case (N1 ) is also true, but another
way is for her to plan indiscriminately to write thank you notes by hand,
by email, by dictation, in which case (N1 ) is not true but (N2 ) still is.
1
I think this is what Simon Blackburn (1988) had in mind.
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Because she disagrees with you, (N3 ) is also true, but it could also be true
if (per impossibile!) Miss Manners had no plans whatsoever involving thank
you notes.
Is Gibbard really entitled to appeal to a sufficiently robust notion of
disagreement? The suspicion is that the notion of a state of mind with
which one might coherently agree or disagree is a notion that has to be
explained. Of course, it is quite intuitive. When you believe in God and I
do not, we disagree; when you have a headache and I do not, we do not
disagree; when I hope the Yankees win and you hope they lose, we disagree;
when you recognize a Schumann lied by the style and I do not, we don’t
disagree. It is quite intuitive, too, that when you plan always to write thank
you notes by hand and I plan to write them indiscriminately by hand and by
email, we disagree in plan. Supporting this intuition is the further intuition
that if I change from my former, indiscriminate plan to your stricter one,
I have changed my mind, whereas when your headache goes away you have
not changed your mind. In Thinking How to Live, Gibbard simply takes the
notion of disagreeing with a state of mind (and the notion of a state of mind
with which one might disagree) as a primitive notion. But this is worrisome.
It’s not that absent an account of disagreement we should worry that there
is no such thing. Rather, the worry is that if we have no explanation for why
some states can be disagreed with and others cannot, then for all we know it
could be that the correct explanation is not amenable to expressivism. For
instance, it could be (for all we know) that the states with which it makes
sense to disagree are the ones that are really representations of independent
fact. No expressivist could then let his account of negation be grounded in
an appeal to the idea of disagreement in attitude.2
3. Hyperplans and Completeness
In Thinking How to Live, Gibbard gives us a new device: a hyperplan, namely,
a fully specified plan for every conceivable contingency. Hyperplans are
complete. They are analogous to possible worlds, which are completely
2
Why not? I think this is a complicated matter. Here’s the short version. A
sophisticated expressivist might be happy to agree that whenever one attitude disagrees
with another, the two attitudes are representations of contrary contents. But no
expressivist should be happy using this way of talking in an explanation. When you and
I disagree in plan, then we disagree about what one ought to do; no problem there. But
contents like one ought to ϕ have to be explained without appeal to ought-laden facts or
properties. So the final explanation of disagreement in (normative) attitude cannot be
in terms of the representational contents of the attitudes. The direction of explanation
must be the other way around.
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specific ways that the world might be. Your opinions can be represented
by a set of possible worlds, and the limiting case of such a set is a single
world. Someone who was unimaginably opinionated would represent the
world as being exactly this way or that, as being precisely this possible world
or that one. Similarly, someone whose plans were unimaginably detailed,
perfectly so, would have a hyperplan. Since hyperplans are complete, every
act whose contradictory is not required by a given hyperplan is thereby
permitted. So, in the context of hyperplans, permission is defined in terms
of requirement, without appeal to external negation. External negation,
then, can be defined in terms of permission and requirement. Hyperplans
solve the problem of primitive disagreement and so the problem of external
negation. How exactly do they manage to do this? By being complete.
Earlier we rejected the idea of defining external negation by appeal to
absence of an attitude. The point was that (N3 ) says that Miss Manners
lacks the requirement attitude toward writing thank you notes by hand,
but that doesn’t mean that she tolerates writing thank you notes by hand,
since she may have no view about the question one way or the other, so
the absence of requirement can’t be what (N2 ) attributes. But there are no
hyperplans that ‘have no view’ about a question. So a hyperplan that fails
to require A a fortiori permits ¬A.
Now appeal to completeness of formal objects, or of the states of an
idealized agent, is tricky in this context, as Unwin (2001) explains in
discussing Gibbard (1990). We have to ask, what is the difference between
a system that is silent on the question of thank you notes and a system that
permits all sorts of ways of writing them? This question is a bit hard to grasp.
It helps if we keep our down-to-earth, unidealized, human perspective in
mind. First, following Unwin, a traffic code is silent about thank you notes
but does not say that email thank you notes are permissible, so silence
and permission aren’t the same. Second, the important question is not
primarily about a formalism, but rather about people and what they are
doing when they think this or that, what attitude they are expressing when
they say one thing or another. For us theorists to speak of complete formal
systems or plans, then, is not enough: we are supposed to say systematically
how to connect a state of mind to a normative sentence. Formal objects
like normative systems can help with book-keeping, but they do not, in
themselves, tell us about states of mind.
An example will illustrate. Suppose Mr Manners has a carefully considered
and quite permissive view about thank you notes: any old way of writing
them, he thinks, is permissible. Officer Lopez, on the other hand, has no
views about thank you notes at all. Her firmly held normative views are
about behavior in traffic. Lopez and Manners are alike in this way: each
lacks the requiring attitude toward hand-written notes, toward emailed
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notes, toward engraved notes, and so forth. Our formalism is capable of the
intuitively correct representation of their normative attitudes, of course. We
want to represent Mr Manners’s attitudes by the collection of all complete
normative systems that permit each type of thank you note (really we
want a proper subset, since he’ll have lots of other normative attitudes that
‘rule out’ many, but for all that’s been said so far the full set will do).
Officer Lopez’s state will include all of those but also the complete systems
that forbid emailed notes, those that require engraved notes, and so forth.
Officer Lopez is undecided, and so she has not ruled out extremely strict
systems of manners, as Mr Manners has. But what is it about the states of
mind of Lopez and Manners as they are that tells us which collection of
formal objects properly models each of their states?
Think of it this way. It does not follow from a plan’s failing to forbid
emailing that the plan permits emailing. That permission does follow from
the plan’s failing to forbid emailing, plus the completeness of the plan.
So permissions are fully defined in terms of restrictions, in the context of
hyperplans. But what fact about a person’s state of mind does the fact of
completeness of the formal object correspond to?
I’ll first explain how a certain solution might work. The idea will turn
on the fact that planning is more ‘decisive’ than having attitudes might be.
Decisiveness of a state is what completeness of plans (considered as formal
objects) models. But then I’ll say how the new model runs into a ‘problem of
no mere permissions’, where ‘mere permissions’ arise in cases in which some
things are permitted without also being required. The new model seems not
to allow for mere permissions. Next, I’ll explain how Gibbard makes room
for some kinds of mere permissions, but not others. My tentative verdict
will be that the missing permissions are ones we can live without. Finally,
though, I’ll argue that the same old problem returns in a new guise, namely,
as the ‘‘no preference problem’’. I have a suggestion for how to solve this
problem. If my suggestion works, it makes expressivism negation-safe. But
I’m not sure that it does work.
4. The Interpretation of Hyperplans and the Problem
of Mere Permissions
Here is how I understand hyperplans. Each hyperplan delivers from each
circumstance a particular thing to do. If there is nothing I plan to do in a
certain circumstance, then my plans are in that respect incomplete; there is
no question of my having a very wishy-washy plan that explicitly declines
to rule anything out. In this respect, planning is by its nature a ‘decisive’
activity, as having attitudes is not. A collection of ‘requiring’ attitudes is not
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unfinished, we might say, merely because it contains no requirement toward
either of a pair of contradictories; a plan is unfinished if it contains no plan
to do anything in a given circumstance. This means that the indeterminacy
between permission and indecision is driven out of the hyperplan model.
Planning and generic normative attitude differ in this way. When I do
not require one action or another, I might be undecided, but I might be
tolerant. If I do not plan to write thank you notes but neither do I plan not
to write any, I am thereby undecided.
Something is forbidden, in the planning model, when an alternative is
planned, and permitted when a complete (hyper)plan doesn’t forbid it. This
means that in the formalism (as I’ve given it so far), everything is required
or forbidden; there are no (mere) permissions. Once we see this, it is clear
why the problem of distinguishing the noncommittal (Officer Lopez) from
the tolerant (Mr Manners) is dissolved: one of the possibilities is eliminated
altogether.
Now on the one hand, the eradication of mere permission seems entirely
in keeping with the spirit of the planning model, but on the other hand it
looks like a problem in its own right. Let’s call it ‘‘the problem of no mere
permissions’’. It’s a problem because we surely want a way to make sense of
the normative judgment that a certain course of action is permitted but not
required. It is in the spirit of the planning model, because when I am decided
my plans just say what to do. They do not say what I am permitted to do
except insofar as what is permitted is also required. Actually, this is not quite
true. It suggests a complication to the planning model. The complication
will reduce, but not eliminate, the problem of no mere permissions.
I am about to go off on some errands. I will stop and get a coffee, and
then I’ll go to the supermarket and pick up some dishwashing liquid. Right
now, I haven’t decided which kind of coffee to get. I’ll either get a venti
iced decaf Americano, or else a triple grande decaf latte. I just can’t make
up my mind yet, because it’s not a hot day but it’s very humid. I’ll decide
later. I also haven’t decided which kind of dishwashing liquid to get, the
yellow or the blue kind. That’s because I don’t think there is any difference
between the two kinds except for the color, and I don’t care which color I
get. Now in each case, one might say that my plans are incomplete, but to
my mind the flavor of the incompleteness is very different. In the case of the
dishwashing liquid, I won’t plan any further, but just grab a bottle when
the time comes. It just doesn’t matter. One might perfectly well say that my
plan is just to grab one, and that I do not plan to grab any particular one is
not a hole in my plan. (Compare: I plan to brush my teeth tonight, but I do
not plan to start brushing left to right and I do not plan to start brushing
right to left.) In the case of the coffee, I am going to make up my mind, or
in any case try, because it does matter which kind I get. Talking to myself in
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5. Hyperplans and the Problem of Supererogation
The model of hyperplans, then, does allow some room for mere permissions.
It doesn’t allow all the room one might want, though. For there are some
mere permissions that are not intuitively accounted for by the relation of
ties, or the attitude of indifference. The clearest cases of resistant mere
permissions are cases of supererogation. Suppose Carl is on his way to a
basketball game, one that he’s been looking forward to for months. As he
sits on the bus looking out the window, he sees a woman fumbling with
some of her belongings, and he watches as she drops her wallet, collects
3
Compare Gibbard (2003: 45) where Sherlock Holmes has weighed up options and
decided that either of two options will do, and when the time comes he opts for one of
them (packing): ‘‘Packing from preference is different from plumping for packing out of
indifference.’’
4
There is some room for worry here. It is perfectly clear that there is a difference
between being indifferent between a pair of options and having failed to form a definite
preference at all. Indifference is as definite as preference and entirely different from
indecision, as the contrast between the dishwashing liquid case and the coffee case shows.
What is somewhat worrisome is the possibility that preference and indifference might
ultimately need an explanation in terms of the agent’s beliefs about what is better than
what. Some of John Broome’s work suggests this possibility; see esp. Broome (1993).
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normative language I might say, ‘‘Either the venti iced decaf Americano, or
else a triple decaf latte is what I ought to get, but I’m not yet sure which; on
the other hand, either color of dishwashing liquid is ok.’’ This difference,
between dishwashing incompleteness and coffee incompleteness, is easy to
accommodate in the planning model; no surprise since I introduced it from
within the planning model. When I just grab the yellow bottle of detergent,
I haven’t really made up my mind in favor of yellow: I could have picked
a blue one without any change of mind. Of course, someone might be the
same way with respect to coffee, but not me! Here’s one way to capture the
difference: between colors of dishwashing liquid I am indifferent, and my
indifference is adequately expressed in a plan that counts buying either as
‘the thing to do’, whereas between coffee types I am rather undecided, and
can’t make up my mind yet which is ‘the drink to buy’.3
In short, plans, even hyperplans, have room for ties. Options that are
tied (for first!) are not severally required, but none of them is forbidden,
either. They are therefore each merely permitted. The difference between
mere permission and indecision is underwritten, in the planning model, by
the difference between the attitude of indifference and the failure to have
any worked out preference at all.4
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the other items she had out and, oblivious, walks on. He cries out, but she
doesn’t hear him. The bus is at a stop. Carl faces a choice. He could stay
on the bus and shout again as it drives by the woman, but that is not very
likely to work. Or he could instead sprint out the door, pick up the wallet,
and give it to her, but if he does that he will miss the first quarter of the
basketball game. What ought Carl to do? What do you plan to do in such a
circumstance?
Here is what I think we intuitively want to say. Carl is permitted to carry
out the first plan. Sprinting off the bus is not required. He is, certainly,
also permitted to carry out the supererogatory second plan: he does nothing
wrong or forbidden by sprinting off the bus and missing the first quarter
of the game. But it does not seem quite right to assimilate Carl’s example
to the example of dishwashing liquid. It’s not that it doesn’t matter which
act Carl performs. It’s not that in forming our own plan we find ourselves
indifferent between the options. The supererogatory act and the merely
obligatory one are not, intuitively, tied for first place. The supererogatory
act is better. It is preferable. In my finest planning moments, I plan definitely
to save the woman’s wallet and, bitterly, miss a quarter of my beloved
basketball game, should I find myself in Carl’s shoes. But then what to
make of the judgment that sitting tight and shouting another time or two
is permissible?
As I am understanding the planning model, it has room for some mere
permissions but no room for the idea of the supererogatory. The model
therefore imposes some restrictions on the sorts of fundamental normative
outlooks that a person can have. If planning just is what’s behind normative
judgment, then there is no coherent judgment of the form, ‘‘A and B are each
permissible, though A is definitely better than B.’’ This seems to be a cost.
It may not be much of a cost, though. The example of Carl is deceptive,
in a way, because it has a distinctly moral cast to it, as indeed all of
the standard examples of supererogation have: supererogation, after all,
is an ethical concept. But Gibbard’s norm expressivism is in the first
instance about the most fundamental category of to-be-doneness, and
only derivatively about moral norms. In Wise Choices, Gibbard called
the fundamental category ‘rationality’ and gave a further, important but
detachable, story about how moral judgment works. In Thinking How
Gibbard brackets the question of whether the most fundamental category
involved in judgments of what to do is the category of rationality, and
indeed he’s noncommittal about whether the concepts he analyzes are
really the ones expressed by the oughts of ordinary English, and there is
not much mention of morality. Now supererogation is deeply engrained
in commonsense thinking about morality, but it is not obviously part of
commonsense thinking about what to do, all things considered. Indeed, the
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coherence of the idea of something’s being worse-but-permissible, just from
the point of view of rationality, is hotly disputed.5 So a model of normative
discourse that rules out rational supererogation, or final question of what to
do supererogation, may not thereby incur much of a cost.
Ethical supererogation, as I said, is a different story, but it may be that
the general sort of approach Gibbard takes to moral discourse is perfectly
able to handle supererogation. Judgments of what is morally permissible
and what is morally best, for instance, might be judgments of what to feel,
and moral sentiments might fit together in a structured way.6 In any case,
the plausibility of commonsense ethical supererogation is not, for all that’s
been said, a problem for norm expressivism.
I am sorry to say that, even if I am right that we can live without rational
supererogation, the resulting model allows the old negation problem to
slip in the back door again. Plans order alternatives; by expelling mere
permissions they answer the question of how to distinguish permissions
from indecision. Ties, introduced as a way of allowing mere permissions
back into the picture, spoil the answer by wrecking the tight relation
between permissions and requirements.
Normative claims express planning states, as Gibbard says. Planning
states, as I understand them, are something like intentions and something
like preferences.7 Let’s look again at our original negations and see what
planning states make them true.
(N1 ) Miss Manners believes one must not write thank you notes
by hand.
(N2 ) Miss Manners believes it is not so that one must write thank
you notes by hand.
(N3 ) Miss Manners does not believe one must write thank you notes
by hand.
The first is true iff Miss Manners plans not to write thank you notes by hand.
Think in terms of preference: Miss Manners prefers not writing thank you
5
I’m thinking of the ‘satisficing’ literature. See esp. Dreier (2004).
See for instance Gibbard’s contribution to this volume.
7
Gibbard’s planning states are not exactly like intentions in the ordinary sense
because we can ‘plan’, as Gibbard uses the word, for circumstances in which we know
we will never find ourselves, and we can ‘plan’ to do things even when we know our
‘planning’ will not bring about the things we ‘plan’. I am not sure exactly how Gibbard’s
‘planning’ differs from preferring.
6
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notes by hand to writing them by hand, according to (N1 ). (N2 ) attributes
to Miss Manners a logically weaker view: it is true iff Miss Manners does
not plan to write thank you notes by hand, that is, so long as she prefers
writing them by hand or is indifferent between writing them by hand and
not. This state is logically weaker because it leaves open the possibility that
Miss Manners is indifferent among the ways of writing thank you notes, so
that, according to her, not writing thank you notes by hand is permissible
but so is writing them by hand. That possibility is ruled out by (the view
attributed to Miss Manners by) (N1 ). Finally, (N3 ) is about what plan or
preference Miss Manners lacks: she does not plan or prefer to write thank
you notes by hand. This last is, properly, consistent with Miss Manners
having no view at all about thank you notes, and is not, of course, the same
as her being indifferent among the ways of writing them.
But why is it not the same? That’s (what I’ll call) the ‘‘no preference
problem’’. There is a distinction, I said, between indifference and indecision,
the two kinds of ‘‘no preference’’, and it is an intuitive difference, as
shown by the contrast between dishwashing liquid (indifference) and coffee
(indecision). But how can this difference be made out in an expressivist
framework? If you ask me on my way to the market which sort of liquid I
prefer, I’ll say I’m indifferent; if you ask me which kind of coffee I want, I’ll
say I haven’t decided. But in drawing the distinction, might I be implicitly
relying on a more realist metaethics that I’m entitled to? I worry that I am.
At the end of section 3, I noted that permissions are defined by the
complete facts of requirements plus the fact of completeness. Those things
are permitted whose complements are not required by complete plans. Then
we can define external negation by the duality laws. But this trick works only
if we have an independent account of completeness. The model of plans that
allow no ties gives us such an independent account, but the model of plans
with ties lets it slip away. To see this, imagine that we are interviewing Bob
about his preferences. He can tell us when he prefers A to B. Sometimes,
when we ask him about a pair of alternatives, he says that he prefers neither.
How can we tell whether his lack of preference is the indifference kind or
the indecision kind? My question isn’t really epistemological. I assume that
if we could get our hands on what fact it is that determines which way
he lacks a preference, then in principle we could find out about that fact.
In any case, it seems to me, this last question is the important one. If it
can be answered, and answered in an expressivist-respectable way, then the
problem of negation is solved, by way of the problem of completeness. But
it is not clear that it can be answered in an expressivist-respectable way.
Maybe the best answer is that the absence of preference is indifference just
in case Bob believes that the alternatives are equally good, and the absence of
preference amounts to indecision just in case Bob has no belief about which
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alternative is better. Myself, I suspect the explanation goes the other way
around. Bob’s beliefs about which alternatives are better are accounted for
by Bob’s preferences. But in that case, the difference between indifference
and lack of preference must be explicable without the help of beliefs about
what is better than what.
7. Defined Indifference: A Suggestion
Someone is defined indifferent between options A and B iff (i) she does
not prefer A to B or B to A, and (ii) for any X, she prefers A to X iff
she prefers B to X and prefers X to A iff she prefers X to B.
I want it to turn out that defined indifference has the right logical
properties to play the role in the expressivist account of negation that
indifference itself was going to play. In the first place, defined indifference
is an equivalence relation. Indifference ought to be an equivalence relation,
too. But lack of preference is not, because it is not transitive. (I am calling
‘lack of preference’ the union, or disjunction, of genuine indifference and
proper indecision. Proper indecision is plainly not an equivalence relation,
because it is not reflexive; nor is it transitive.) I may be undecided between
buying an iced Americano for $2 and buying a latte for $3, and also
undecided between buying the latte for $3 and the Americano for $2.10,
but I definitely prefer buying the Americano for $2 to buying it for $2.10.
That is why lack of preference is not transitive.8 The same example shows
how ordinary, intuitive cases of indecision are kept out of the domain of
defined indifference. For even though I do not prefer the Americano for $2
8
In general, the union of two transitive relations need not be transitive, but that is
not the point here. The transitivity failure of indecision is inherited by lack of preference.
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My suggestion for a solution to the no preference problem starts with a
piece of technical apparatus, which I’ll call defined indifference. Before I
give the definition, here are a few words of explanation. First, I am not
claiming to be defining the ordinary language use of ‘indifferent’. Instead
I am introducing a technical notion to be used in the expressivist account
of negation. I do think the defined notion comes pretty close to capturing
one sense of ‘indifference’, at least in that it is close to being necessarily
coextensive with the ordinary notion. Second, I will use preference, but
not indifference, in the definition. I am taking preference for granted.
My problem is to get indifference (or a stand-in) distinguished from the
indecisive form of lack of preference, and for this purpose it is acceptable to
take preference itself, the definite kind of preference, as a primitive.
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to the latte for $3, nor the latte for $3 to the Americano for $2, my attitudes
toward the two do not satisfy the second clause of defined indifference,
since there is some X, namely the cheaper Americano, which I prefer to
the $2.10 Americano but not to the latte. The intuitive idea is that you
cannot be properly indifferent between two options if there is something
you prefer (or disprefer) to one and not to the other. To be indifferent
is to rank the two together, so that each is below everything the other is
below, and each is above everything the other is above. In this way defined
indifference resembles indifference.
So far so good, but now comes a hitch. When someone is genuinely
indifferent between a pair of options, she will also be defined indifferent
between them, but the converse may not be true. There are counterexamples, and they may be serious ones, because they may ruin the prospect
of using defined indifference to solve the negation problem.
Lily is, by stipulation, completely indecisive, but she also turns out to
be maximally defined indifferent. For each pair of options, Lily is defined
indifferent between them. This is because everything she prefers to one she
prefers also to the other, for the reason (not intended in our definition) that
there is nothing she prefers to either; similarly, there is nothing to which she
prefers one item but not the other.
Now Lily is a very, very peculiar creature. She is an extreme, degenerate
example of a preferring agent. If defined indifference does not match
the ordinary notion of indifference for a being like Lily, maybe that
is OK. After all, I do not need to insist that defined indifference is
indifference, nor even that it exactly matches the extension, for every
possible agent, of indifference. Still, the example of Lily is theoretically
problematic. I cannot claim that defined indifference represents indifference
in an expressivist account of normative judgment. For Lily’s attitudes are
like those of Officer Lopez (in section 3 above) and not like those of
Mr Manners, and we said there must be a difference between those
attitudes, so there must be a difference between Lily’s preferences and the
perfectly indifferent preference structure. But Lily turns out to be defined
indifferent between every pair.
If the Thoroughly Indecisive Example were the only counter-example to
the suggestion, maybe an expressivist could swallow it; maybe our intuitions
deceive us and there is in fact no difference between the normative outlook
of extreme limits of the collections of attitudes of Officer Lopez and Mr
Manners. But there is another counter-example.
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The Thoroughly Indecisive Example: Lily can’t make up her mind
about anything. For any pair of options, she has no preference between
them. She is not indifferent; rather, she is utterly indecisive.
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The problem is that although there are many things that Henry prefers to
getting a ham sandwich, like avoiding nuclear war, maintaining sovereignty,
and so on, he naturally prefers all of those things also to getting a tuna
sandwich; similarly there are many things to which he prefers getting a
ham sandwich, like nuclear war and giving up national sovereignty, but he
prefers tuna to those things, too. Henry has a Big Important preference
structure, and tucked into the middle of it he has a little bubble of indecision
regarding unimportant (but not negligible) matters. Henry turns out to be
defined indifferent, then, between tuna and ham, although we stipulated
that he is undecided between them.
What has gone wrong with my apparatus of defined indifference? It
relies on there being a sufficiently rich field of preference to guarantee
that something or other will be wedged beneath or above any given item,
but very close to it. If there is, then the wedged object will be neither
above nor below the item to be paired with the given one. In my leading
example, I added a saving of 10 cents to the Americano, plausibly very
close in an ordinary person’s preference structure, so close as not to make
enough difference to yield a definite preference between the money-saving
Americano and the latte. For ordinary preferences, it is safe to assume a
rich structure, but in theory a person’s preference field could be severely
impoverished, either overall, as Lily’s, or locally, as Henry’s. Call this the
Problem of the Impoverished Field.
I cannot stipulate that everyone has a rich field of preference, and I
cannot rely on the fact that real people do have rich fields. It is not up to
me what preferences people can possibly have, and since my suggestion is
offered to expressivists as an aid to their explanation for what it is to have
this or that normative view, I have to be sure that it works in theory for
possible as well as actual preferences.
8. Some Untidy Last Thoughts
Fertilizer: inserting lotteries to enrich the field
It is hard to imagine someone with very severely impoverished preference
structure. It may be harder to imagine than you think. You know obsessive
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The Example of Momentous and Trivial Choices: Henry is mainly
concerned with affairs of state. He prefers avoiding nuclear war to
engaging in it. He prefers maintaining his nation’s sovereignty to
losing it. And he has many other preferences of enormous national
importance. Right now, though, he has to order lunch, and he can’t
make up his mind. Ham, or tuna? He is undecided.
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people, and maybe you can in imagination increase someone’s obsessiveness
until you imagine them single minded, or like Henry so generally absorbed
with enormous issues as to leave sterile little pockets in their field. But
we can ask about some artificial objects of preference, objects engineered
to enrich the field of preference in just the way we need. These hunks of
fertilizer are the so-called ‘lotteries’ of decision theory fame.
Ask Henry whether there are things he prefers to a ham sandwich
that he doesn’t prefer to a tuna sandwich, and he can’t think of any.
He can only think of the momentous affairs of state, all of which he
enormously prefers to either sandwich or enormously disprefers. But take
one such momentously good object, say the prospect of rapprochement
with Cuba, and divide its desirability (to Henry) by a large number. Offer
Henry the ham sandwich augmented by a one millionth chance of the
rapprochement—that is, tell him (convince him) that if he takes the ham
sandwich, the prospects of coming to terms with Cuba will be enhanced
by one in a million. Does this tiny extra something get him to prefer ham
to tuna? What if the enhancement were a one in a billion enhancement?
One in ten to the thousandth power? Henry is defined indifferent, recall,
only if there is nothing he prefers to a ham sandwich that he doesn’t prefer
to a tuna sandwich. Plainly any tiny enhancement to the ham prospect will
bring it above the plain ham sandwich, so if there is any such tiny enhanced
ham prospect that he doesn’t prefer to the tuna prospect, Henry must be
undecided and not indifferent.
Lottery fertilizer is nice because it comes in continuous quantities. If
a certain enhancement is too large, you can always cut it in half. We
should keep in mind that there are other enhancements that can act as
field fertilizer, even though they do not have the continuity of lotteries. For
example, we could offer to donate one penny to Oxfam if Henry gets the
ham sandwich. Or, again exploiting a ready-made continuum, we could
threaten to postpone one of the Momentous Goods by a day, or a minute,
or a tenth of a second, . . . if Henry orders tuna.
Add enough fertilizer to the field and it becomes more and more
difficult to imagine Henry being genuinely undecided between the kinds of
sandwich even though no comparison can separate them. Maybe the bare,
unimaginable possibility of that sort of indecision can be shrugged off by
an expressivist. Maybe an expressivist can say that in such a case Henry
does believe each kind of sandwich is permissible, or that there is simply
no determinate fact as to whether he regards each kind as permissible or
instead has no view yet. I’m not confident that the fertilizer strategy makes
it possible to shrug off the counter-examples, but it does seem to make the
bullet easier for an expressivist to bite.
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One objection to the fertilizer strategy is that it can simply be stipulated
away. Finish the story like this: Henry does not think about lotteries and
never considers conjunctions of sandwich prospects with tiny chances of
momentous prospects, since those conjunctions are of no possible practical
interest and Henry doesn’t for a moment think that anybody can really
make the prospect of rapprochement with Cuba be more likely conditional
on Henry’s lunch. He therefore has no preferences at all among such things.
He is undecided, though not in the sense that he’s thought and thought
and thought about the sandwiches and just can’t make up his mind. And
we can similarly stipulate away any thoughts of monetary or temporal
commensuration of the momentous and trivial prospects.
There seems to me to be something fishy about this objection. When we
impute preferences to agents, we do not in general suppose that the agents
have entertained explicitly the comparison we have in mind. I know that
my sister prefers a spectacular view of the Grand Canyon to being immersed
in icy water for ten minutes. True, I might express this knowledge by saying
that she would prefer the view to the immersion, but I don’t merely know
that she would, I know that she does. By contrast, I know that my son would
prefer eggplant to caviar if only he were to try them, but he does not now
have any such preference.
People have preferences that they’ve never considered just as they have
beliefs they have never entertained, like the belief that 123,000,000,000
is not a prime number. These preferences and beliefs may be analyzable
as dispositions to believe or prefer under the right circumstances. If they
are, though, they will have to be distinguished somehow from dispositions
to believe and prefer things that we do not actually believe and prefer,
eggplants to caviar or a moderately obvious but obscure theorem of
Euclidean geometry. It may be difficult to distinguish the never-consideredit kind of lack of preference from indifference, in some cases, but perhaps
this is no objection to an expressivist program. After all, it may be similarly,
analogously difficult to distinguish the state of lacking any normative view
about a certain subject from the state of having a quite permissive view
about the subject.
9. Conclusion/Recap
The problem of negation, that is, the problem of explaining what in
general is expressed by the negation of a sentence expressing a given
attitude, is made more tractable by the model of hyperplans proffered
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Imputed intentional states
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in Thinking How to Live. On the simplest account, hyperplanning rules
out the possibility of mere permissions by its very structure. Allowing
ties, thought of as representing indifference, into plans recaptures the
possibility of mere permissions. It does not allow for supererogation, but,
I’ve argued, it is not obvious that supererogation enters normative thinking
on the ground floor, and the higher tiers might be built up from the
foundation in ways that can plausibly account for ethical supererogation.
Indifference, however, must be distinguished from indecision, and the task
of distinguishing them looks a lot like the original task of explaining the
difference between negating an attitude and just lacking it. I suggested that
‘defined indifference’, picked out by some auxiliary clauses guaranteeing
transitivity, would do as an approximation of the ordinary notion of
indifference. Some difficulties show up at the margins of possibility, making
defined indifference indistinguishable from indecision when the agent’s
field of preference is radically impoverished, either globally or just locally,
but I gave some reasons to think that the difficulties are not too serious.
Blackburn, Simon, ‘Attitudes and Contents’, Ethics, 98 (1988), 501–17.
Broome, John, ‘Can a Humean be Moderate?’, in R. G. Frey and Christopher Morris
(eds.), Value, Welfare and Morality (Cambridge: Cambridge University Press,
1993), 51–73.
Dreier, James, ‘Why Ethical Satisficing Makes Sense and Rational Satisficing
Doesn’t’, in Michael Byron (ed.), Satisficing and Maximizing (Cambridge, Mass.:
Cambridge University Press, 2004), 131–54.
Gibbard, Allan, Wise Choices, Apt Feelings (Cambridge, Mass.: Harvard University
Press, 1990).
Thinking How to Live (Cambridge, Mass.: Harvard University Press, 2003).
Hale, Bob, ‘On the Logic of Attitudes’, in J. Haldane and C. Wright (eds.), Reality:
Representation and Projection (Oxford: Oxford University Press, 1993), 337–63,
385–8.
Unwin, Nicholas, ‘Quasi-Realism, Negation and the Frege-Geach Problem’, Philosophical Quarterly, 49 (1999), 337–52.
‘Norms and Negation: A Problem for Gibbard’s Logic’, Philosophical Quarterly,
51 (2001), 60–75.
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REFERENC ES
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Queries in Chapter 8
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Q1. For ‘R’ and ‘P’ we have used caligraphic font. Please confirm if the
font is fine
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